![]() ![]() Repeat this process until you can find no more preemptive sets, or until the Sudoku rule is violated or there is a cell whose markup is empty (contains no numbers).Ī. Whenever you enter a number, use the current color, i.e. Try to use methods 2 and 3 again if you were able to cross out numbers from the markups of any cells. Whenever you have found a preemptive set, cross out numbers in the markups of cells whenever the occupancy theorem allows it. Try to break preemptive sets with several elements down into smaller preemptive sets. ![]() Look at each column, row and 3x3 box and try to break it down into preemptive sets. Note the current cell, the number you entered and the color of the pen on a separate sheet of paper.Ħ. Assign the current cell a colored pen that you have not used before. Choose an empty cell, call it the "current cell" and enter a number from its markup. If neither is the case, then proceed to step 5.ĥ. If you violated the Sudoku condition, then the Sudoku does not have any solutions and you are done.Ĭ. If you have solved the Sudoku puzzle,then you are done.ī. Repeat this process until you can find no more preemptive sets, or until the Sudoku rule is violated.Ī. Whenever you have found a preemptive set, cross out numbers in the markups of cells whenever the Occupancy theorem allows it. Use methods 2 and 3 alternatingly to complete the puzzle as much as you can, until those methods lead no further.Ģ. ![]() Crook’s method of preemptive sets reduces the number of combinations in a clever way.ġ. Our simple solving algorithm can solve everything, but is not very easy to do for humans, because there are so many combinations to check. Remember that the candidate-checking and place-finding methods are nice and fast, but sometimes fail. Ĭrook uses a hybrid approach, which is a sophistated combination of our simple solving algorithm, the place-finding method, the candidate-checking method, and the method of preemptive sets, which we will learn about in a minute. The following discussion is in part adapted from his paper “A Pencil-and-Paper Algortihm for Solving Sudoku Puzzles”, which is available at. James Crook, professor emiritus of Computer Science at Winthrop University, came up with an algorithm that will solve any Sudoku puzzle, and can be done on paper. You probably noticed in the previous activity that there are indeed Sudokus that cannot be solved using method 2 or 3. ![]()
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